Anna University Applied Mathematics for Electrical Engineers syllabus for ME Power Electronics and Drives Department. The subject code for Applied Mathematics for Electrical Engineers subject is MA7163.
- Subject Credit : 4
- Regulation : 2013
- Department : POWER ELECTRONICS AND DRIVES
- Subject Name : Applied Mathematics for Electrical Engineers - AMEE
- Subject Code : MA7163
OBJECTIVES:
- To develop the ability to apply the concepts of Matrix theory and Linear programming in Electrical Engineering problems.
- To achieve an understanding of the basic concepts of one dimensional random variables and apply in electrical engineering problems.
- To familiarize the students in calculus of variations and solve problems using Fourier transforms associated with engineering applications.
UNIT I MATRIX THEORY (9+3)
The Cholesky decomposition - Generalized Eigen vectors, Canonical basis - QR factorization - Least squares method - Singular value decomposition.
UNIT II CALCULUS OF VARIATIONS (9+3)
Concept of variation and its properties – Euler’s equation – Functional dependant on first and higher order derivatives – Functionals dependant on functions of several independent variables – Variational problems with moving boundaries – problems with constraints - Direct methods: Ritz and Kantorovich methods.
UNIT III ONE DIMENSIONAL RANDOM VARIABLES (9+3)
Random variables - Probability function – moments – moment generating functions and their
properties – Binomial, Poisson, Geometric, Uniform, Exponential, Gamma and Normal distributions – Function of a Random Variable.
UNIT IV LINEAR PROGRAMMING (9+3)
Formulation – Graphical solution – Simplex method – Two phase method - Transportation and Assignment Models
UNIT V FOURIER SERIES (9+3)
Fourier Trigonometric series: Periodic function as power signals – Convergence of series –
Even and odd function: cosine and sine series – Non-periodic function: Extension to other intervals - Power signals: Exponential Fourier series – Parseval’s theorem and power spectrum – Eigen value problems and orthogonal functions – Regular Sturm-Liouville systems – Generalized Fourier series.
TOTAL: 60 PERIODS
REFERENCES:
1. Richard Bronson, “Matrix Operation”, Schaum’s outline series, 2nd Edition, McGraw Hill, 2011.
2. Gupta, A.S., Calculus of Variations with Applications, Prentice Hall of India Pvt. Ltd., New Delhi, 1997.
3. Oliver C. Ibe, “Fundamentals of Applied Probability and Random Processes, Academic Press, (An imprint of Elsevier), 2010.
4. Taha, H.A., “Operations Research, An introduction”, 10th edition, Pearson education, New Delhi, 2010.
5. Andrews L.C. and Phillips R.L., Mathematical Techniques for Engineers and Scientists, Prentice Hall of India Pvt.Ltd., New Delhi, 2005.
6. Elsgolts, L., Differential Equations and the Calculus of Variations, MIR Publishers, Moscow, 1973.
7. Grewal, B.S., Higher Engineering Mathematics, 42nd edition, Khanna Publishers, 2012.
8. O'Neil, P.V., Advanced Engineering Mathematics, Thomson Asia Pvt. Ltd., Singapore, 2003.
9. Johnson R. A. and Gupta C. B., “Miller & Freund’s Probability and Statistics for Engineers”, Pearson Education, Asia, 7th Edition, 2007.
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